what is the integral of x/(1+x^2)^2 dx This is a question of a past AP exam of calculus BC

i know i have to use the substitution method where u=(1+x^2), du=2xdx. I have to find the integral but i'm just focused on the coefficient because i get a different answer for that part

then you set the integral to .5(int)1/u^2 du,

but my answer choice on the AP exam test says that instead of 1/2 as the coefficient, it's 1/4 and i don't see where the 4 comes from.